Exact calculation: fractions, surds and π worksheet — GCSE Foundation

1.Work out 3π − π, giving your answer as a multiple of π.

2.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

3.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

4.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

5.A circle has a diameter of 10 cm. Work out the exact circumference of the circle, in terms of π.

6.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

7.Work out 5/6 × 2/9, giving your answer in its simplest form.

8.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

9.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

10.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.

11.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

12.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

13.Work out 4π + 2π, giving your answer as a multiple of π.

14.Work out 2/3 × 3/4 exactly, giving your answer in its simplest form.

15.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?